Familien komplexer räume zu gegebenen infinitesimalen deformationen

Let M be a domain in the complex plane, :XM a flat family of reduced complex spaces, (X_o, _o) the fibre over a point OM, and x_o the sheaf of (1,O)-forms over X_o. The family defines an element (Ext¹ (_Xo, _o))_x for every point xX. We prove: If (X_o, _o) is a normal complex space, x a point in X_o such that (Ext² (_Xo, _o))_x=O, then for each infinitesimal deformation (Ext¹ (_Xo, _o))_x there exists a flat reduced family with =. This statement is analogous to a result of KODAIRA-NIRENBERG-SPENCER in the theory of deformations of compact complex manifolds.